Introduction to proteomics data analysis
9 April 2020
Contents
1 Background
This case-study is a subset of the data of the 6th study of the Clinical Proteomic Technology Assessment for Cancer (CPTAC). In this experiment, the authors spiked the Sigma Universal Protein Standard mixture 1 (UPS1) containing 48 different human proteins in a protein background of 60 ng/\(\mu\)L Saccharomyces cerevisiae strain BY4741. Two different spike-in concentrations were used: 6A (0.25 fmol UPS1 proteins/\(\mu\)L) and 6B (0.74 fmol UPS1 proteins/\(\mu\)L) [5]. We limited ourselves to the data of LTQ-Orbitrap W at site 56. The data were searched with MaxQuant version 1.5.2.8, and detailed search settings were described in Goeminne et al. (2016) [1]. Three replicates are available for each concentration.
2 Data
We first import the peptides.txt file. This is the file that contains your peptide-level intensities. For a MaxQuant search [6], this peptides.txt file can be found by default in the “path_to_raw_files/combined/txt/” folder from the MaxQuant output, with “path_to_raw_files” the folder where raw files were saved. In this tutorial, we will use a MaxQuant peptides file from MaxQuant that can be found on the pdaData repository. We will use the MSnbase package to import the data.
We generate the object peptideFile with the path to the peptides.txt file. In this file we will fetch the data from the github repository linked to the pda course: https://statomics.github.io/pda. You can also replace the peptideFile with a string that points to the path of a file on your local hard drive. With the grepEcols function we find the columns that are containing the expression data of the peptides in the peptides.txt file.
library(tidyverse)
library(limma)
library(Features)
library(msqrob2)
myurl <- "https://raw.githubusercontent.com/statOmics/pda/data/quantification/cptacAvsB_lab3/peptides.txt"
peptidesFile <- myurl
ecols <- MSnbase::grepEcols(peptidesFile, "Intensity ", split = "\t")
pe <- readFeatures(table = peptidesFile, fnames = 1, ecol = ecols,
name = "peptide", sep="\t")We can extract the spikein condition from the raw file name. It is the 12 character if the name.
cond <- which(strsplit(colnames(pe)[[1]][1], split = "")[[1]] == "A") # find where condition is stored
colData(pe)$condition <- substr(colnames(pe), cond, cond) %>% unlist %>% as.factorWe calculate how many non zero intensities we have per peptide. This will be useful for filtering.
rowData(pe[["peptide"]])$nNonZero <- rowSums(assay(pe[["peptide"]]) > 0)Peptides with zero intensities are missing peptides and should be represent with a NA value instead of 0.
pe <- zeroIsNA(pe)2.1 Data exploration
We can inspect the missingness in our data with the plotNA() function provided with MSnbase. 45% of all peptide intensities are missing and for some peptides we don’t even measure a signal in any sample. The missingness is similar across samples. Note, that we plot the peptide data, so the label protein in the plot refers to peptides.
MSnbase::plotNA(assay(pe))3 Preprocessing
We will log transform, normalize, filter and summarize the data.
3.1 Log transform the data
pe <- logTransform(pe, base = 2)
limma::plotDensities(assay(pe[["peptide"]]))
3.2 Filtering
3.2.1 Handling overlapping protein groups
In our approach a peptide can map to multiple proteins, as long as there is none of these proteins present in a smaller subgroup.
pe[["peptide"]]<-pe[["peptide"]][rowData(pe[["peptide"]])$Proteins %in% msqrob2::smallestUniqueGroups(rowData(pe[["peptide"]])$Proteins),]3.2.2 Remove reverse sequences (decoys) and contaminants
We now remove the contaminants, peptides that map to decoy sequences and proteins, which were only identified by peptides with modifications.
pe[["peptide"]] <- pe[["peptide"]][rowData(pe[["peptide"]])$Reverse!= "+", ]
pe[["peptide"]] <- pe[["peptide"]][rowData(pe[["peptide"]])$
Potential.contaminant!="+", ]3.2.3 Remove peptides of proteins that were only identified with modified peptides
I will skip this step for the moment. Large protein groups file needed for this.
3.2.4 Drop peptides that were only identified in one sample
We want to keep peptide that were at least observed twice.
pe[["peptide"]] <- pe[["peptide"]][rowData(pe[["peptide"]])$nNonZero >= 2, ]
nrow(pe[["peptide"]])## [1] 7011We keep 7011 peptides upon filtering.
3.3 Quantile normalize the data
assay(pe[["peptide"]]) <- limma::normalizeQuantiles(assay(pe[["peptide"]]))3.4 Explore quantile normalized data
Upon normalisation the density curves for all samples coincide.
limma::plotDensities(assay(pe[["peptide"]]))
We can visualize our data using a Multi Dimensional Scaling plot, eg. as provided by the limma package.
limma::plotMDS(assay(pe[["peptide"]]), col = as.numeric(colData(pe)$condition))
The first axis in the plot is showing the leading log fold changes (differences on the log scale) between the samples. We notice that the leading differences (log FC) in the peptide data seems to be driven by technical variability. Indeed the samples do not seem to be clearly separated according to the spike in condition.
3.5 Summarization to protein level
Use the standard sumarisation in aggregateFeatures ( robust summarisation).
pe <- aggregateFeatures(pe, fcol = "Proteins", na.rm = TRUE, name="protein")## Your data contains missing values. Please read the relevant section
## in the aggregateFeatures manual page for details the effects of
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## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match## Warning in rlm.default(X, expression, ...): 'rlm' failed to converge in 20
## steps## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
## Warning in rlm.default(X, expression, ...): some of ... do not match
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## Warning in rlm.default(X, expression, ...): some of ... do not matchWe notice that the leading differences (log FC) in the protein data is still according to technical variation. On the second dimension, however, we also observe a clear separation according to the spike-in condition. Hence, the summarization that accounts for peptide specific effects makes the effects due to the spike-in condition more prominent!
plotMDS(assay(pe[["protein"]]),col = as.numeric(colData(pe)$condition))
4 Data Analysis
4.1 Estimation
rowData(pe[["protein"]])$model <- msqrob2::msqrobLm(pe[[ "protein"]], ~condition,colData=colData(pe))4.2 Inference
L <- as.matrix(c(0, 1))
rownames(L) <- rowData(pe[["protein"]])$model[[1]] %>% msqrob2::getCoef() %>% names
rowData(pe[["protein"]])$b_a <- msqrob2::topTable(rowData(pe[["protein"]])$model, L)4.3 Plots
4.3.1 Volcano-plot
volcano <- ggplot(rowData(pe[["protein"]])$b_a, aes(x = logFC, y = -log10(pval),
color = adjPval < 0.05)) +
geom_point(cex = 2.5) + scale_color_manual(values = alpha(c("black", "red"), 0.5)) + theme_minimal()
volcano
4.3.2 Heatmap
We first select the names of the significant proteins.
sigNames <- rowData(pe[["protein"]])$b_a %>% rownames_to_column("protein") %>% filter(adjPval<0.05) %>% pull(protein)
heatmap(assay(pe[["protein"]])[sigNames, ])
5 Detail plots
We first extract the normalized peptide expression values for a particular protein.
for (protName in sigNames)
{
pePlot <- pe[protName, ]
pePlotDf <- data.frame(longFormat(pePlot))
pePlotDf$assay <- factor(pePlotDf$assay,
levels = c("peptide", "protein"))
pePlotDf$condition <- as.factor(colData(pePlot)[pePlotDf$colname, "condition"])
p1 <- ggplot(data = pePlotDf,
aes(x = colname,
y = value,
group = rowname)) +
geom_line() + geom_point() + theme_minimal() +
facet_grid(~ assay) + ggtitle(protName)
print(p1)
p2 <- ggplot(pePlotDf, aes(x = colname, y = value, fill = condition)) + geom_boxplot(outlier.shape = NA) +
geom_point(position = position_jitter(width = .1), aes(shape = rowname)) + scale_shape_manual(values = 1:nrow(pePlotDf)) +
labs(title = protName, x = "sample", y = "Peptide intensity (log2)") + theme_minimal()
facet_grid(~assay)
print(p2)
}
